Theorems · Theorem · group theory
inv_mul_cancel
∀ {G : Type u_1} [inst : Group G] (a : G), a⁻¹ * a = 1- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 107 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 31 definitions · uses no axioms
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Group.inv_mul_cancelproof · cited by 1
Cited by109
Results whose statement or proof uses this declaration.
- mul_inv_cancelproof · cited by 128
- map_invproof · cited by 95
- inv_mul_cancel_leftproof · cited by 88
- inv_smul_smulproof · cited by 76
- inv_mul_cancel_rightproof · cited by 70
- Group.isUnitproof · cited by 18
- zpow_add_oneproof · cited by 18
- isConj_iffproof · cited by 16
- Representation.inv_self_applyproof · cited by 12
- mul_eq_one_iff_eq_invproof · cited by 12
- one_le_mabsproof · cited by 11
- Subgroup.comap_map_eqproof · cited by 9